3k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Centre National de la Recherche ScientifiqueFR60 papers
- Kootenay Association for Science & TechnologyCA40 papers
- Chinese Academy of SciencesCN33 papers
- Texas A&M UniversityUS32 papers
- RWTH Aachen UniversityDE30 papers
- King Fahd University of Petroleum and MineralsSA29 papers
- TU WienAT25 papers
- National University of SingaporeSG24 papers
- The University of Texas at AustinUS24 papers
- University of OxfordGB23 papers
- Georgia Institute of TechnologyUS22 papers
- Aix-Marseille UniversitéFR20 papers
20 papers · 2 filters
Residual-based a posteriori error estimation for multipoint flux mixed finite element methods
Shaohong Du, Shuyu Sun, Xiaoping Xie
A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimen…
Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
Julio E. Castrillon-Candas, Fabio Nobile, Raul F. Tempone
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a rand…
Reduced temporal convergence rates in high-order splitting schemes
M. T. Warnez, B. K. Muite
Recently-derived high-order splitting schemes with complex coefficients are shown to exhibit reduced convergence rates for certain parabolic evolution equations. When applied to se…
Error Analysis of Explicit Partitioned Runge-Kutta Schemes for Conservation Laws
Willem Hundsdorfer, David I. Ketcheson, Igor Savostianov
An error analysis is presented for explicit partitioned Runge-Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or ti…
Numerical Modeling of Nanoparticles Transport with Two-Phase Flow in Porous Media Using Iterative Implicit Method
M. F. El-Amin, Jisheng Kou, Shuyu Sun +1
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brow…
On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability
Jesús Sierra, Aslan Kasimov, Peter Markowich +1
We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates. The stationary…
Two-dimensional wave propagation in layered periodic media
Manuel Quezada de Luna, David I. Ketcheson
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive eff…
Propagation of internal errors in explicit Runge--Kutta methods and internal stability of SSP and extrapolation methods
David I. Ketcheson, Lajos Lóczi, Matteo Parsani
In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example…
Fast Multipole Preconditioners for Sparse Matrices Arising from Elliptic Equations
Huda Ibeid, Rio Yokota, Jennifer Pestana +1
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures…
Strong Stability Preserving Multistep Runge-Kutta Methods
Christopher Bresten, Sigal Gottlieb, Zachary Grant +3
High-order spatial discretizations with strong stability properties (such as monotonicity) are desirable for the solution of hyperbolic PDEs. Methods may be compared in terms of th…
The Closest Point Method and multigrid solvers for elliptic equations on surfaces
Yujia Chen, Colin B. Macdonald
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equati…
A combined finite volume--nonconforming finite element scheme for compressible two phase flow in porous media
Bilal Saad, Mazen Saad
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion te…
Space Decompositions and Solvers for Discontinuous Galerkin Methods
Blanca Ayuso de Dios, Ludmil Zikatanov
We present a brief overview of the different domain and space decomposition techniques that enter in developing and analyzing solvers for discontinuous Galerkin methods. Emphasis i…
A comparison of high order explicit Runge-Kutta, extrapolation, and deferred correction methods in serial and parallel
David I. Ketcheson, Umair bin Waheed
We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge--Kutta pairs. We consider orders four…
Rational functions with maximal radius of absolute monotonicity
Lajos Loczi, David I. Ketcheson
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions…
Upscaling of Nonlinear Forchheimer Flows
Eugenio Aulisa, Lidia Bloshanskaya, Yalchin Efendiev +1
In this work we propose upscaling method for nonlinear Forchheimer flow in highly heterogeneous porous media. The generalized Forchheimer law is considered for incompressible and s…
Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling
Y. Efendiev, J. Galvis, R. Lazarov +2
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. W…
Analysis of the Discontinuous Petrov-Galerkin Method with Optimal Test Functions for the Reissner-Mindlin Plate Bending Model
Victor M. Calo, Nathaniel O. Collier, Antti H. Niemi
We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid va…
Spatially partitioned embedded Runge-Kutta methods
David I. Ketcheson, Colin B. Macdonald, Steven J. Ruuth
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different p…
Generalized Multiscale Finite Element Methods (GMsFEM)
Yalchin Efendiev, Juan Galvis, Thomas Y. Hou
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separatio…